Numerical solutions of the reaction diffusion system by using
exponential cubic B-spline collocation algorithms

• Authors: Ozlem Ersoy , Idris Dag
• Languages of publication: EN

Abstracts

EN

The solutions of the reaction-diffusion system
are given by method of collocation based on the exponential
B-splines. Thus the reaction-diffusion systemturns
into an iterative banded algebraic matrix equation. Solution
of the matrix equation is carried out byway of Thomas
algorithm. The present methods test on both linear and
nonlinear problems. The results are documented to compare
with some earlier studies by use of L∞ and relative
error norm for problems respectively.

Keywords

EN

finite element method; collocation method; reaction-diffusion equations; exponential cubic B-spline; nonlinear differential equation

• Publisher: De Gruyter Open
• Journal: Open Physics
• Year: 2015
• Volume: 13
• Issue: 1

Dates

received

17 - 8 - 2015

accepted

22 - 11 - 2015

online

31 - 12 - 2015

Contributors

author

Ozlem Ersoy

• Mathematics-Computer Department, Eskisehir
  Osmangazi University, 26480, Eskisehir, Turkey

author

Idris Dag

• Mathematics-Computer Department, Eskisehir
  Osmangazi University, 26480, Eskisehir, Turkey

References

• [1] M. Rodrigo, M. Mimura, Japan J. Indust. Appl. Math. 18, 657(2001)
• [2] B.J. McCartin, J. Approx. Theory 66, 1 (1991)
• [3] M. Sakai, R.A. Usmani, Numer. Math. 55, 493 (1989)
• [4] D. Radunovic, Numer. Algor. 47, 191 (2008)
• [5] S. Chandra Sekhara Rao, Mukesh Kumar, Appl. Numer. Math.58, 1572 (2008)[Crossref]
• [6] R. Mohammadi, Appl. Math. 4, 933 (2013)[Crossref]
• [7] I. Dag, O. Ersoy, Advances in Numerical Analysis 2015, 1 (2015)
• [8] A. Sahin, I. Dag, B. Saka, Kybernetes 37, 326 (2008)
• [9] R.C. Mittal, R.K. Jain, Mathematical Sciences 7, 12 (2013)
• [10] B.K. Singh, G. Arora, Mathematics in Engineering Science andAerospace 5, 2 (2014)
• [11] R.I. Fernandes, G. Fairweather, J. Comput. Phys. 231, 6248(2012)
• [12] W. Cai, W. Zhang, J. Comput. Phys. 139, 92 (1998)
• [13] A. Sahin, Ph.D. Thesis, Department of Mathematics, EskisehirOsmangazi University, Eskisehir (2009)
• [14] M. Abbas, A.A. Majid, A.I.Md. Ismail, A. Rashid, PLoS ONE 9, 1(2014)
• [15] C.S. Chaou, Y.T. Zhang, R. Zhao, Q. Nie, Descrete Cont. Dyn.-B 7,515 (2007)
• [16] I. Prigogine, R. Lefever, J. Chem. Phys. 48, 1695 (1968)
• [17] E.H. Twizell, Y. Wang, W.G. Price,F. Fakhr, Numer. Meth. Part. D.E. 10, 435 (1994)
• [18] J.H. Merkin, D.J. Needham, S.K. Scott, Proc. R. Soc. Lond. A 427,187 (1989)
• [19] D.G. Aronson, H.F. Weinberger, Lecture Notes in Mathematics,Springer Verlag, Heidelberg, Berlin, 446, 5 (2006)
• [20] S.L. Wu, S.Y. Liu, Appl. Math. Model. 33, 2757 (2009)[Crossref]

Identifiers

DOI

10.1515/phys-2015-0047